--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: ROB022-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB022-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Robbins Algebra *)
+
+(* Problem : c + -c=c => Boolean *)
+
+(* Version : [Win90] (equality) axioms. *)
+
+(* English : If there is an element c such that c + -c = c then the *)
+
+(* algebra is Boolean. *)
+
+(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(* : [McC92] McCune (1992), Email to G. Sutcliffe *)
+
+(* Source : [McC92] *)
+
+(* Names : - [McC92] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v2.2.1, 0.33 v2.2.0, 0.29 v2.1.0, 0.75 v2.0.0 *)
+
+(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 5 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : Commutativity, associativity, and Huntington's axiom *)
+
+(* axiomatize Boolean algebra. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms for Robbins algebra *)
+
+(* Inclusion of: Axioms/ROB001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : ROB001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Robbins algebra *)
+
+(* Axioms : Robbins algebra axioms *)
+
+(* Version : [Win90] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(* Source : [OTTER] *)
+
+(* Names : Lemma 2.2 [Win90] *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
+
+(* Number of literals : 3 ( 3 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 2 ( 0 constant; 1-2 arity) *)
+
+(* Number of variables : 7 ( 0 singleton) *)
+
+(* Maximal term depth : 6 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_huntingtons_axiom:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀c:Univ.
+∀negate:∀_:Univ.Univ.
+∀H0:eq Univ (add c (negate c)) c.
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#a.
+#add.
+#b.
+#c.
+#negate.
+#H0.
+#H1.
+#H2.
+#H3.
+nauto by H0,H1,H2,H3;
+nqed.
+
+(* -------------------------------------------------------------------------- *)